A) \[12{{x}^{2}}-4{{y}^{2}}-24ax+9{{a}^{2}}=0\]
B) \[12{{x}^{2}}+4{{y}^{2}}-24ax+9{{a}^{2}}=0\]
C) \[12{{x}^{2}}-4{{y}^{2}}+24ax+9{{a}^{2}}=0\]
D) \[12{{x}^{2}}+4{{y}^{2}}+24ax+|9{{a}^{2}}=0\]
Correct Answer: A
Solution :
Let centre of the circle is, \[C=(h,k)\] and radius = r |
Co-ordinates of \[A\equiv \left[ \frac{ah}{a+r},\frac{ak}{a+r} \right]\] |
Co-ordinates of \[B\equiv \left[ \frac{2ar+2ah}{2a+r},\frac{2ak}{2a+r} \right]\] |
Putting co-ordinates of A and B in \[{{S}_{1}},{{S}_{2}}\]respectively and eliminating r, \[12{{x}^{2}}-4{{y}^{2}}-24ax+9{{a}^{2}}=0\] |
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